Subgroups — C₁₉×#17751 #18023710

Order 4864.

996 conjugacy classes of subgroups.

The subgroup lattice has 532 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#533	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#2920	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₉×#423	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#1561	C₂	1	4	yes	maximal, complemented
5	C₁₉×#1552	C₂	1	4	yes	maximal, complemented
6	C₁₉×#1549	C₂	1	2	yes	maximal, complemented
7	C₁₉×#1546	C₂	1	2	yes	maximal, complemented
8	C₂²×M₁₆×C₁₉	—	2	1	no	—
9	C₁₉×#533	—	2	1	no	—
10	C₁₉×#533	—	2	1	no	—
11	C₁₉×#533	—	2	1	no	—
12	C₁₉×#533	—	2	1	no	—
13	C₁₉×#533	C₄	1	2	yes	—
14	C₁₉×#533	C₄	1	2	yes	—
15	C₁₉×#533	C₂²	1	2	yes	—
16	C₁₉×#533	C₂²	1	2	yes	—
17	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
18	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
19	C₂×C₁₉×#125	C₄	1	2	yes	—
20	C₂×C₁₉×C₂²⋊Q₈	—	2	1	no	—
21	C₂×C₁₉×C₂²⋊Q₈	—	2	1	no	—
22	C₂×C₄×Q₈×C₁₉	—	2	1	no	—
23	C₂×C₄×Q₈×C₁₉	—	2	1	no	—
24	C₂×C₁₉×#117	C₄	1	2	yes	—
25	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
26	C₁₉×#432	—	2	1	no	—
27	C₁₉×#432	C₂²	1	2	yes	—
28	C₁₉×#431	—	2	1	no	—
29	C₁₉×#431	C₂²	1	2	yes	—
30	C₁₉×#423	—	2	1	no	—
31	C₁₉×#423	—	2	1	no	—
32	C₁₉×#423	C₂²	1	2	yes	—
33	C₁₉×#423	C₂²	1	2	yes	—
34	C₁₉×#423	C₂²	1	2	yes	—
35	C₂×C₁₉×C₄⋊C₈	—	2	1	no	—
36	C₂×C₁₉×C₄⋊C₈	C₂²	1	2	yes	—
37	C₁₉×#407	—	2	1	no	—
38	C₄×M₁₆×C₁₉	—	2	1	no	—
39	C₁₉×#332	C₂²	1	8	yes	complemented
40	C₁₉×#332	C₂²	1	8	yes	complemented
41	C₂²×Q₈×C₁₉	—	2	1	no	—
42	C₂²×Q₈×C₁₉	—	2	1	no	—
43	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
44	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
45	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
46	C₂×M₁₆×C₁₉	—	2	2	no	—
47	C₂×M₁₆×C₁₉	—	2	2	no	—
48	C₂×M₁₆×C₁₉	—	2	2	no	—
49	C₂×M₁₆×C₁₉	—	4	4	no	—
50	C₂²×C₈×C₁₉	—	2	2	no	—
51	C₁₉×C₄⋊Q₈	—	2	1	no	—
52	C₁₉×C₄⋊Q₈	—	2	1	no	—
53	C₁₉×C₄⋊Q₈	—	2	1	no	—
54	C₁₉×C₄⋊Q₈	—	2	1	no	—
55	C₁₉×C₄⋊Q₈	C₂×C₄	1	2	yes	—
56	C₁₉×C₄⋊Q₈	C₂×C₄	1	2	yes	—
57	C₁₉×C₄⋊Q₈	C₂³	1	2	yes	—
58	C₁₉×C₄⋊Q₈	C₂³	1	2	yes	—
59	C₁₉×#125	—	2	2	no	—
60	C₁₉×#125	—	2	2	no	—
61	C₁₉×#125	C₂×C₄	1	4	yes	—
62	C₁₉×#125	C₂×C₄	1	4	yes	—
63	C₁₉×C₂²⋊Q₈	—	2	2	no	—
64	C₁₉×C₂²⋊Q₈	—	2	2	no	—
65	C₁₉×C₂²⋊Q₈	—	2	2	no	—
66	C₁₉×C₂²⋊Q₈	—	2	2	no	—
67	C₁₉×C₂²⋊Q₈	—	2	2	no	—
68	C₁₉×C₂²⋊Q₈	—	2	2	no	—
69	C₁₉×C₂²⋊Q₈	—	2	2	no	—
70	C₁₉×C₂²⋊Q₈	—	2	2	no	—
71	C₄×Q₈×C₁₉	—	2	2	no	—
72	C₄×Q₈×C₁₉	—	2	2	no	—
73	C₄×Q₈×C₁₉	—	2	2	no	—
74	C₄×Q₈×C₁₉	—	2	2	no	—
75	C₄×Q₈×C₁₉	—	2	2	no	—
76	C₄×Q₈×C₁₉	—	2	2	no	—
77	C₄×Q₈×C₁₉	—	2	2	no	—
78	C₄×Q₈×C₁₉	—	2	2	no	—
79	C₁₉×#117	—	2	2	no	—
80	C₁₉×#117	—	2	2	no	—
81	C₁₉×#117	C₂×C₄	1	4	yes	—
82	C₁₉×#117	C₂×C₄	1	4	yes	—
83	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
84	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
85	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
86	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
87	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
88	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
89	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
90	C₂×C₄²×C₁₉	—	2	2	no	—
91	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
92	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
93	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
94	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
95	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
96	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
97	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
98	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
99	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
100	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
101	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
102	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
103	C₁₉×C₄⋊C₈	—	2	2	no	—
104	C₁₉×C₄⋊C₈	—	2	2	no	—
105	C₁₉×C₄⋊C₈	—	2	2	no	—
106	C₁₉×C₄⋊C₈	—	2	2	no	—
107	C₁₉×C₄⋊C₈	C₂³	1	4	yes	—
108	C₁₉×C₄⋊C₈	C₂³	1	4	yes	—
109	C₁₉×C₂²⋊C₈	—	2	2	no	—
110	C₁₉×C₂²⋊C₈	—	2	2	no	—
111	C₁₉×#97	—	2	2	no	—
112	C₄×C₈×C₁₉	—	2	2	no	—
113	C₂⁴×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
114	C₂×Q₈×C₁₉	—	2	2	no	—
115	C₂×Q₈×C₁₉	—	2	2	no	—
116	C₂×Q₈×C₁₉	—	2	2	no	—
117	C₂×Q₈×C₁₉	—	2	2	no	—
118	C₂×Q₈×C₁₉	—	4	4	no	—
119	C₂×Q₈×C₁₉	—	4	2	no	—
120	C₂×Q₈×C₁₉	—	4	2	no	—
121	C₂²×C₄×C₁₉	—	2	4	no	—
122	C₂²×C₄×C₁₉	—	2	2	no	—
123	C₂²×C₄×C₁₉	—	2	2	no	—
124	C₂²×C₄×C₁₉	—	2	2	no	—
125	C₂²×C₄×C₁₉	—	2	2	no	—
126	C₂²×C₄×C₁₉	—	4	2	no	—
127	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
128	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
129	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
130	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
131	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
132	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
133	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
134	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
135	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
136	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
137	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
138	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
139	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
140	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
141	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
142	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
143	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
144	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
145	M₁₆×C₁₉	—	4	4	no	—
146	M₁₆×C₁₉	—	4	4	no	—
147	M₁₆×C₁₉	—	4	4	no	—
148	C₂×C₈×C₁₉	—	2	4	no	—
149	C₂×C₈×C₁₉	—	2	4	no	—
150	C₂×C₈×C₁₉	—	4	4	no	—
151	C₄⋊C₄×C₁₉	—	2	4	no	—
152	C₄⋊C₄×C₁₉	—	2	4	no	—
153	C₄⋊C₄×C₁₉	—	2	4	no	—
154	C₄⋊C₄×C₁₉	—	2	4	no	—
155	C₄⋊C₄×C₁₉	—	2	2	no	—
156	C₄⋊C₄×C₁₉	—	2	2	no	—
157	C₄⋊C₄×C₁₉	—	2	2	no	—
158	C₄⋊C₄×C₁₉	—	2	2	no	—
159	C₄⋊C₄×C₁₉	—	2	2	no	—
160	C₄⋊C₄×C₁₉	—	2	2	no	—
161	C₄⋊C₄×C₁₉	C₂²×C₄	1	4	yes	—
162	C₄⋊C₄×C₁₉	C₂²×C₄	1	4	yes	—
163	C₂²⋊C₄×C₁₉	—	2	4	no	—
164	C₂²⋊C₄×C₁₉	—	2	4	no	—
165	C₄²×C₁₉	—	2	4	no	—
166	C₄²×C₁₉	—	2	4	no	—
167	C₄²×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
168	C₄²×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
169	C₄²×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
170	C₄²×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
171	C₄²×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
172	C₄²×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
173	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
174	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
175	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
176	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
177	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
178	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
179	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
180	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
181	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
182	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
183	#17751	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
184	C₂³×C₁₉	—	2	2	no	—
185	C₂³×C₁₉	—	2	2	no	—
186	C₂³×C₁₉	—	4	1	no	—
187	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
188	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
189	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
190	Q₈×C₁₉	—	4	4	no	—
191	Q₈×C₁₉	—	4	2	no	—
192	Q₈×C₁₉	—	4	2	no	—
193	Q₈×C₁₉	—	4	4	no	—
194	Q₈×C₁₉	—	4	4	no	—
195	C₂×C₄×C₁₉	—	2	2	no	—
196	C₂×C₄×C₁₉	—	2	2	no	—
197	C₂×C₄×C₁₉	—	2	1	no	—
198	C₂×C₄×C₁₉	—	2	1	no	—
199	C₂×C₄×C₁₉	—	2	1	no	—
200	C₂×C₄×C₁₉	—	2	1	no	—
201	C₂×C₄×C₁₉	—	2	2	no	—
202	C₂×C₄×C₁₉	—	2	2	no	—
203	C₂×C₄×C₁₉	—	2	2	no	—
204	C₂×C₄×C₁₉	—	2	2	no	—
205	C₂×C₄×C₁₉	—	2	2	no	—
206	C₂×C₄×C₁₉	—	2	2	no	—
207	C₂×C₄×C₁₉	—	2	2	no	—
208	C₂×C₄×C₁₉	—	2	2	no	—
209	C₂×C₄×C₁₉	—	2	2	no	—
210	C₂×C₄×C₁₉	—	2	4	no	—
211	C₂×C₄×C₁₉	—	2	4	no	—
212	C₂×C₄×C₁₉	—	4	1	no	—
213	C₂×C₄×C₁₉	—	4	1	no	—
214	C₂×C₄×C₁₉	—	4	1	no	—
215	C₂×C₄×C₁₉	—	4	4	no	—
216	C₂×C₄×C₁₉	—	4	4	no	—
217	C₂×C₄×C₁₉	#101	1	4	yes	—
218	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
219	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
220	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
221	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
222	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
223	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
224	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
225	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
226	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
227	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
228	C₂×C₄×C₁₉	#137	1	2	yes	—
229	C₂×C₄×C₁₉	C₂³×C₄	1	1	yes	characteristic
230	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
231	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
232	C₈×C₁₉	—	4	4	no	—
233	C₈×C₁₉	—	4	4	no	—
234	C₂×#533	C₂×C₁₉	1	1	yes	characteristic
235	#2920	C₂×C₁₉	1	1	yes	characteristic
236	C₂×#423	C₂×C₁₉	1	1	yes	characteristic
237	#1561	C₂×C₁₉	1	4	yes	complemented
238	#1552	C₂×C₁₉	1	4	yes	complemented
239	#1549	C₂×C₁₉	1	2	yes	complemented
240	#1546	C₂×C₁₉	1	2	yes	complemented
241	C₂²×C₁₉	—	2	1	no	—
242	C₂²×C₁₉	—	2	1	no	—
243	C₂²×C₁₉	—	2	1	no	—
244	C₂²×C₁₉	—	2	1	no	—
245	C₂²×C₁₉	—	2	1	no	—
246	C₂²×C₁₉	—	2	1	no	—
247	C₂²×C₁₉	—	2	1	no	—
248	C₂²×C₁₉	—	4	4	no	—
249	C₂²×C₁₉	C₂×#101	1	2	yes	—
250	C₂²×C₁₉	#417	1	2	yes	—
251	C₂²×C₁₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
252	C₄×C₁₉	—	2	1	no	—
253	C₄×C₁₉	—	2	1	no	—
254	C₄×C₁₉	—	2	1	no	—
255	C₄×C₁₉	—	2	1	no	—
256	C₄×C₁₉	—	2	1	no	—
257	C₄×C₁₉	—	2	1	no	—
258	C₄×C₁₉	—	2	1	no	—
259	C₄×C₁₉	—	4	4	no	—
260	C₄×C₁₉	—	4	4	no	—
261	C₄×C₁₉	C₂×#101	1	2	yes	—
262	C₄×C₁₉	C₂×#101	1	2	yes	—
263	C₄×C₁₉	#417	1	2	yes	—
264	C₄×C₁₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
265	C₄×C₁₉	C₂×#137	1	1	yes	characteristic
266	C₄×C₁₉	#575	1	2	yes	—
267	C₂²×M₁₆	—	2	1	no	—
268	#533	—	2	1	no	—
269	#533	—	2	1	no	—
270	#533	—	2	1	no	—
271	#533	—	2	1	no	—
272	#533	C₄×C₁₉	1	2	yes	—
273	#533	C₄×C₁₉	1	2	yes	—
274	#533	C₂²×C₁₉	1	2	yes	—
275	#533	C₂²×C₁₉	1	2	yes	—
276	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
277	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
278	C₂×#125	C₄×C₁₉	1	2	yes	—
279	C₂×C₂²⋊Q₈	—	2	1	no	—
280	C₂×C₂²⋊Q₈	—	2	1	no	—
281	C₂×C₄×Q₈	—	2	1	no	—
282	C₂×C₄×Q₈	—	2	1	no	—
283	C₂×#117	C₄×C₁₉	1	2	yes	—
284	C₂²×C₄²	C₂²×C₁₉	1	1	yes	characteristic
285	#432	—	2	1	no	—
286	#432	C₂²×C₁₉	1	2	yes	—
287	#431	—	2	1	no	—
288	#431	C₂²×C₁₉	1	2	yes	—
289	#423	—	2	1	no	—
290	#423	—	2	1	no	—
291	#423	C₂²×C₁₉	1	2	yes	—
292	#423	C₂²×C₁₉	1	2	yes	—
293	#423	C₂²×C₁₉	1	2	yes	—
294	C₂×C₄⋊C₈	—	2	1	no	—
295	C₂×C₄⋊C₈	C₂²×C₁₉	1	2	yes	—
296	#407	—	2	1	no	—
297	C₄×M₁₆	—	2	1	no	—
298	#332	C₂²×C₁₉	1	8	yes	complemented
299	#332	C₂²×C₁₉	1	8	yes	complemented
300	C₂×C₁₉	—	2	2	no	—
301	C₂×C₁₉	—	2	2	no	—
302	C₂×C₁₉	—	4	1	no	—
303	C₂×C₁₉	C₂²×#101	1	1	yes	characteristic
304	C₂×C₁₉	C₂×#417	1	1	yes	characteristic
305	C₂×C₁₉	#2896	1	1	yes	characteristic
306	C₂²×Q₈	—	2	1	no	—
307	C₂²×Q₈	—	2	1	no	—
308	C₂³×C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
309	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
310	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
311	C₂×M₁₆	—	2	2	no	—
312	C₂×M₁₆	—	2	2	no	—
313	C₂×M₁₆	—	2	2	no	—
314	C₂×M₁₆	—	4	4	no	—
315	C₂²×C₈	—	2	2	no	—
316	C₄⋊Q₈	—	2	1	no	—
317	C₄⋊Q₈	—	2	1	no	—
318	C₄⋊Q₈	—	2	1	no	—
319	C₄⋊Q₈	—	2	1	no	—
320	C₄⋊Q₈	C₂×C₄×C₁₉	1	2	yes	—
321	C₄⋊Q₈	C₂×C₄×C₁₉	1	2	yes	—
322	C₄⋊Q₈	C₂³×C₁₉	1	2	yes	—
323	C₄⋊Q₈	C₂³×C₁₉	1	2	yes	—
324	#125	—	2	2	no	—
325	#125	—	2	2	no	—
326	#125	C₂×C₄×C₁₉	1	4	yes	—
327	#125	C₂×C₄×C₁₉	1	4	yes	—
328	C₂²⋊Q₈	—	2	2	no	—
329	C₂²⋊Q₈	—	2	2	no	—
330	C₂²⋊Q₈	—	2	2	no	—
331	C₂²⋊Q₈	—	2	2	no	—
332	C₂²⋊Q₈	—	2	2	no	—
333	C₂²⋊Q₈	—	2	2	no	—
334	C₂²⋊Q₈	—	2	2	no	—
335	C₂²⋊Q₈	—	2	2	no	—
336	C₄×Q₈	—	2	2	no	—
337	C₄×Q₈	—	2	2	no	—
338	C₄×Q₈	—	2	2	no	—
339	C₄×Q₈	—	2	2	no	—
340	C₄×Q₈	—	2	2	no	—
341	C₄×Q₈	—	2	2	no	—
342	C₄×Q₈	—	2	2	no	—
343	C₄×Q₈	—	2	2	no	—
344	#117	—	2	2	no	—
345	#117	—	2	2	no	—
346	#117	C₂×C₄×C₁₉	1	4	yes	—
347	#117	C₂×C₄×C₁₉	1	4	yes	—
348	C₂×C₄⋊C₄	—	2	2	no	—
349	C₂×C₄⋊C₄	—	2	2	no	—
350	C₂×C₄⋊C₄	—	2	1	no	—
351	C₂×C₄⋊C₄	—	2	1	no	—
352	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	2	yes	—
353	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	2	yes	—
354	C₂×C₂²⋊C₄	—	2	2	no	—
355	C₂×C₄²	—	2	2	no	—
356	C₂×C₄²	C₂×C₄×C₁₉	1	1	yes	characteristic
357	C₂×C₄²	C₂×C₄×C₁₉	1	1	yes	characteristic
358	C₂×C₄²	C₂×C₄×C₁₉	1	1	yes	characteristic
359	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
360	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
361	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
362	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
363	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
364	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
365	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
366	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
367	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
368	C₄⋊C₈	—	2	2	no	—
369	C₄⋊C₈	—	2	2	no	—
370	C₄⋊C₈	—	2	2	no	—
371	C₄⋊C₈	—	2	2	no	—
372	C₄⋊C₈	C₂³×C₁₉	1	4	yes	—
373	C₄⋊C₈	C₂³×C₁₉	1	4	yes	—
374	C₂²⋊C₈	—	2	2	no	—
375	C₂²⋊C₈	—	2	2	no	—
376	#97	—	2	2	no	—
377	C₄×C₈	—	2	2	no	—
378	C₁₉	#17751	1	1	yes	characteristic, direct product factor, Sylow
379	C₂⁴	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
380	C₂×Q₈	—	2	2	no	—
381	C₂×Q₈	—	2	2	no	—
382	C₂×Q₈	—	2	2	no	—
383	C₂×Q₈	—	2	2	no	—
384	C₂×Q₈	—	4	4	no	—
385	C₂×Q₈	—	4	2	no	—
386	C₂×Q₈	—	4	2	no	—
387	C₂²×C₄	—	2	2	no	—
388	C₂²×C₄	—	2	2	no	—
389	C₂²×C₄	—	2	4	no	—
390	C₂²×C₄	—	2	2	no	—
391	C₂²×C₄	—	2	2	no	—
392	C₂²×C₄	—	4	2	no	—
393	C₂²×C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
394	C₂²×C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
395	C₂²×C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
396	C₂²×C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
397	C₂²×C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
398	C₂²×C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
399	C₂²×C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
400	C₂²×C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
401	C₂²×C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
402	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
403	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
404	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
405	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
406	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
407	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
408	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
409	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
410	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
411	M₁₆	—	4	4	no	—
412	M₁₆	—	4	4	no	—
413	M₁₆	—	4	4	no	—
414	C₂×C₈	—	2	4	no	—
415	C₂×C₈	—	2	4	no	—
416	C₂×C₈	—	4	4	no	—
417	C₄⋊C₄	—	2	4	no	—
418	C₄⋊C₄	—	2	4	no	—
419	C₄⋊C₄	—	2	4	no	—
420	C₄⋊C₄	—	2	4	no	—
421	C₄⋊C₄	—	2	2	no	—
422	C₄⋊C₄	—	2	2	no	—
423	C₄⋊C₄	—	2	2	no	—
424	C₄⋊C₄	—	2	2	no	—
425	C₄⋊C₄	—	2	2	no	—
426	C₄⋊C₄	—	2	2	no	—
427	C₄⋊C₄	C₂²×C₄×C₁₉	1	4	yes	—
428	C₄⋊C₄	C₂²×C₄×C₁₉	1	4	yes	—
429	C₂²⋊C₄	—	2	4	no	—
430	C₂²⋊C₄	—	2	4	no	—
431	C₄²	—	2	4	no	—
432	C₄²	—	2	4	no	—
433	C₄²	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
434	C₄²	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
435	C₄²	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
436	C₄²	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
437	C₄²	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
438	C₄²	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
439	C₄²	C₂²×C₄×C₁₉	1	1	yes	characteristic
440	C₄²	C₂²×C₄×C₁₉	1	1	yes	characteristic
441	C₄²	C₂²×C₄×C₁₉	1	1	yes	characteristic
442	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
443	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
444	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
445	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
446	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
447	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
448	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
449	C₂³	—	2	2	no	—
450	C₂³	—	2	2	no	—
451	C₂³	—	4	1	no	—
452	C₂³	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
453	C₂³	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
454	C₂³	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
455	Q₈	—	4	4	no	—
456	Q₈	—	4	4	no	—
457	Q₈	—	4	2	no	—
458	Q₈	—	4	2	no	—
459	Q₈	—	4	4	no	—
460	C₂×C₄	—	2	2	no	—
461	C₂×C₄	—	2	2	no	—
462	C₂×C₄	—	2	2	no	—
463	C₂×C₄	—	2	2	no	—
464	C₂×C₄	—	2	2	no	—
465	C₂×C₄	—	2	2	no	—
466	C₂×C₄	—	2	2	no	—
467	C₂×C₄	—	2	2	no	—
468	C₂×C₄	—	2	1	no	—
469	C₂×C₄	—	2	1	no	—
470	C₂×C₄	—	2	1	no	—
471	C₂×C₄	—	2	1	no	—
472	C₂×C₄	—	2	2	no	—
473	C₂×C₄	—	2	2	no	—
474	C₂×C₄	—	2	2	no	—
475	C₂×C₄	—	2	4	no	—
476	C₂×C₄	—	2	4	no	—
477	C₂×C₄	—	4	1	no	—
478	C₂×C₄	—	4	1	no	—
479	C₂×C₄	—	4	1	no	—
480	C₂×C₄	—	4	4	no	—
481	C₂×C₄	—	4	4	no	—
482	C₂×C₄	C₁₉×#101	1	4	yes	—
483	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
484	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
485	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
486	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
487	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
488	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
489	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
490	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
491	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
492	C₂×C₄	C₁₉×AGL(1,ℤ/8)	1	2	yes	—
493	C₂×C₄	C₁₉×#137	1	2	yes	—
494	C₂×C₄	C₂³×C₄×C₁₉	1	1	yes	characteristic
495	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
496	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
497	C₈	—	4	4	no	—
498	C₈	—	4	4	no	—
499	C₂²	—	2	1	no	—
500	C₂²	—	2	1	no	—
501	C₂²	—	2	1	no	—
502	C₂²	—	2	1	no	—
503	C₂²	—	2	1	no	—
504	C₂²	—	2	1	no	—
505	C₂²	—	2	1	no	—
506	C₂²	—	4	4	no	—
507	C₂²	C₂×C₁₉×#101	1	2	yes	—
508	C₂²	C₁₉×#417	1	2	yes	—
509	C₂²	C₂²×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
510	C₄	—	2	1	no	—
511	C₄	—	2	1	no	—
512	C₄	—	2	1	no	—
513	C₄	—	2	1	no	—
514	C₄	—	2	1	no	—
515	C₄	—	2	1	no	—
516	C₄	—	2	1	no	—
517	C₄	—	4	4	no	—
518	C₄	—	4	4	no	—
519	C₄	C₂×C₁₉×#101	1	2	yes	—
520	C₄	C₂×C₁₉×#101	1	2	yes	—
521	C₄	C₁₉×#417	1	2	yes	—
522	C₄	C₂×C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
523	C₄	C₂×C₁₉×#137	1	1	yes	characteristic
524	C₄	C₁₉×#575	1	2	yes	—
525	C₂	—	2	2	no	—
526	C₂	—	2	2	no	—
527	C₂	—	4	1	no	—
528	C₂	C₂²×C₁₉×#101	1	1	yes	characteristic
529	C₂	C₂×C₁₉×#417	1	1	yes	characteristic
530	C₂	C₁₉×#2896	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂²×C₂²⋊C₄
commutator	C₂×C₄	C₂³×C₄×C₁₉
Frattini, cosocle	C₄²	C₂⁴×C₁₉
prime radical	C₂⁴×C₁₉	C₂²⋊C₄
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂²×C₄²×C₁₉ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
4. C₁₉×#1561	C₂	semidirect
5. C₁₉×#1552	C₂	semidirect
6. C₁₉×#1549	C₂	semidirect
7. C₁₉×#1546	C₂	semidirect
39. C₁₉×#332	C₂²	semidirect
40. C₁₉×#332	C₂²	semidirect
183. #17751	C₁₉	direct (N × H)
237. #1561	C₂×C₁₉	semidirect
238. #1552	C₂×C₁₉	semidirect
239. #1549	C₂×C₁₉	semidirect
240. #1546	C₂×C₁₉	semidirect
298. #332	C₂²×C₁₉	semidirect
299. #332	C₂²×C₁₉	semidirect
378. C₁₉	#17751	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₁₉×#533	2
C₁₉×#2920	2
C₂×C₁₉×#423	2
C₁₉×#1561	2
C₁₉×#1552	2
C₁₉×#1549	2
C₁₉×#1546	2
#17751	19

Subgroups — C19×#17751 #18023710

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#17751 #18023710